“You make me sound like a whore,” the movie star Bradley Cooper said, sitting with his sock feet hanging over the edge of a bed.

Alas, we were not sharing charged banter in his hotel room downtown, but 20 feet away from each other in a chilly rehearsal studio on 42nd Street in Manhattan, along with a director, three other actors, a publicist, a stage manager and a smattering of crew members.

Mr. Cooper, his muscular form covered in baggy gray pants and a T-shirt, his mouth screwed into an O that rendered his famous face utterly unrecognizable, was reciting a line from “The Elephant Man” — the 1977 Bernard Pomerance play inspired by the trying adulthood of Joseph Carey Merrick — that has been a guiding light for him since adolescence.

Merrick is like a rare, irregular coin: Though long out of circulation, he has been sought, turned over and polished by an ardent band of enthusiasts. Born in 1862, he had mysterious and considerable physical deformities that made him an outcast, a freak-show attraction, a medical curiosity and, after his death at 27, an enduring literary subject.

Along with the play, which begins previews on Nov. 7 at the Booth Theater for a 14-week Broadway run, there are multiple books about Merrick, including one misnaming him John, which stuck, by Frederick Treves, the doctor who treated him; a 1980 David Lynch film, starring John Hurt in elaborate prosthetics; a shout-out in a mournful Rufus Wainwright song; and “Elephant!,” a musical spoof from the 1989 movie “The Tall Guy” (with one number titled, rather wickedly, “He’s Packing His Trunk”).

Mr. Cooper himself is not renouncing his sense of humor because he is playing someone so spectacularly disfigured — quite the contrary. “Have a cup of tea before you go?” he ad-libbed, a squeaky Monty Python version of the English accent he’s assuming, to a fellow actor. “It takes me a while to make a cup of tea,” he went on, dolorously, to sniggers from the assembled.

Appearing the evening before on “The Tonight Show” to promote the production, trying to describe how he’d examined Merrick’s skeleton for research purposes, Mr. Cooper had collapsed (with the host, Jimmy Fallon) into a laughing fit that lasted over 10 minutes. (Wearing matching visors, they also spent time crushing eggs against their foreheads, bro style.)

But “The Elephant Man,” which is directed by Scott Ellis on a modest budget of $3 million, is serious business for the actor: a scoop of earth following his gradual but precipitous soar into the showbiz stratosphere, with its thinner, giddy-making air.

It’s also his first appearance on Broadway since 2006, when he supported Julia Roberts, then a star of much greater magnitude, in “Three Days of Rain.” Ben Brantley in The New York Times called that performance “alternately perky and indignant in the manner of a sitcom actor doing testy and aggrieved.”

“I’m a much different person now than I was then,” Mr. Cooper said.

A backward baseball cap on his head, he had compressed his 6-foot-1 frame into a corner booth at a TriBeCa restaurant. He is no longer a sitcom actor but firmly entrenched on the movie-industry A-list, having followed the “Hangover” trilogy, which has earned a reported $1.4 billion worldwide, with back-to-back Oscar-nominated roles in David O. Russell’s “Silver Linings Playbook” and “American Hustle.”

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Bradley Cooper at the Booth Theater.CreditDamon Winter/The New York Times

Along with steadier work, there are perks: Last May, Mr. Cooper interrupted filming of Clint Eastwood’s “American Sniper,” in which he plays the formidably lethal member of the Navy SEALs, Chris Kyle, to act as co-chairman of the Metropolitan Museum of Art’s Costume Institute gala. (His 22-year-old girlfriend, the British model Suki Waterhouse, arrived separately.) Also that month, he formed a production company with Todd Phillips, the “Hangover” director, whom he calls a mentor.

Mr. Eastwood seems to be playing that role, too: “In him, I sort of see myself at certain stages of my career,” Mr. Eastwood wrote in an email, referring to Mr. Cooper. “His work ethic is unparalleled, and he has a concentration level that’s uncommon. I think Bradley’s a tribute to this particular generation of actors. In general, they seem somewhat more serious than my generation was, but I think he’s at the top of that list.”

Alighting briefly on Broadway has become a rite of passage for celebrities perhaps eager to counter their forced depictions in Us Weekly and Just Jared with displays of seriousness. (Daniel Craig, James Franco and Michelle Williams have all touched down there lately.)

Mr. Cooper is not just the glittering ornament in his theatrical ensemble but also its behind-the-scenes orchestrator. He suggested the production to Mr. Ellis for a slot two years ago at the Williamstown Theater Festival, where they had collaborated earlier on Theresa Rebeck’s play “The Understudy.” He told Patricia Clarkson upon their first meeting, at the premiere of the Woody Allen movie “Whatever Works,” that he wanted only her for the role of Madge Kendal, the actress who provides romantic redemption for Merrick. He wooed her further with text messages.

“It was very flattering and sexy,” Ms. Clarkson said on the phone, and she insisted that their version of the play would not disappoint Mr. Cooper’s teeny-bopper fans, if the Williamstown audience had been any indication. “I think young girls who came were so rocked out by the journey that he took them on that they left the theater as older women,” she said.

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Mr. Cooper with Julia Roberts in “Three Days of Rain” (2006).CreditJoan Marcus

As he faces down his own 40th birthday in January, Mr. Cooper acknowledges that he is less settled, physically at least, than ever before.

His life is “truly nomadic now,” he said. He kept his light-blue eyes, perhaps the most cited on a matinee idol since Paul Newman’s, angled in the general direction of the tablecloth. “Those eyes can look a little unpredictable or scary, those big blue eyes,” Mr. Russell said later by telephone. “He can look like he’s got a wild hare in him and then suddenly becomes very tender.”

At the restaurant, though, Mr. Cooper was centered, neutral, calm — and not just because he was experimenting, as many of his peers are these days, with meditation. “I kind of feel cleansed,” he said of his time being Merrick. “I feel full. I feel relaxed. I find it therapeutic, playing him, inhabiting him every day.”

Mr. Cooper has long credited the movie version of “The Elephant Man,” which he saw when he was 12 growing up outside Philadelphia, with his fierce desire to act. “Lynch created a character with John Hurt that was sort of innocent and beautiful and effortlessly benevolent, and there was something so moving about him, given all of his adversity, that just crushed me, as a kid,” he said. “I just felt so akin to him.”

That a comparatively coddled suburbanite could relate to Merrick reveals, perhaps, the unfathomable shadings of teenage psychology. His father, Charles J. Cooper, who died in 2011, was a stockbroker for Merrill Lynch. “I would be lying if I didn’t say that hanging out with Clint doesn’t feel like hanging out with my dad, because they are very similar, just their mannerisms, so comfortable in their skin, and confident, and with an easy way of being that you don’t see men have these days,” Mr. Cooper said.

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Mr. Cooper as Chris Kyle in “American Sniper.”CreditKeith Bernstein

He has always been very close to his mother, Gloria Campano; his older sister, Holly, is a legal assistant who maintains Bradley’s Facebook fan site.

“He’s always been kind of shiny,” said Brian Klugman, a fellow actor who co-directed Mr. Cooper, a friend since they attended Germantown Academy, in “The Words,” a 2012 Sundance entry. “I’d go to his house, and he’d cook something, and then I’d go home and try to cook it and set my house on fire.”

Mr. Cooper, though, said that his artistic ambition “was always met with a bit of a smirk” from his intimates, and that he didn’t get to express his feelings until he underwent actual psychotherapy, when he was still struggling for parts in Los Angeles. “I found it to be a very fulfilling process,” he said. “Especially growing up in an environment where none of that was ever condoned, let alone talked about.”

While doing graduate work at the Actors Studio Drama School, he proposed performing “The Elephant Man” for his master’s thesis. “Why don’t you do something else?” he said, imitating skeptical advisers. “Why don’t you play the Gentleman Caller in ‘The Glass Menagerie’?”

But he insisted, saving money from working the graveyard shift at Morgans Hotel to buy a Tower Air ticket to London, where he saw the hospital where Merrick was treated (“since sort of dismembered”); viewed his cloak and birth certificate; and walked across Whitechapel Road to the address where he exhibited himself (“now a sari store”).

Back in London this summer, he did more research while also working on a film, one in which he’ll play a chef, as he did on the short-lived Fox series “Kitchen Confidential.” He has converted the roof of his house in Los Angeles into a garden, hoping for fresh vegetables by spring. Asked what he had made in the kitchen recently, he replied, “Halibut on a bed of bok choy and mushrooms and then sort of string calamari on top of it.”

Still, though dinner service had begun, Mr. Cooper, who said he had lost 30 of the 40 pounds he gained to play Kyle, had ordered only coffee, and though gender politics have advanced considerably, this reporter did not feel like snarfing down a plate of French fries in front of People’s Sexiest Man Alive of 2011.

The actor said that despite such honors — and the breathless chronicling of his outings with Ms. Waterhouse — he is not overly harassed by an adoring public. “I take the subway everywhere,” he said, though “if I wear a hat and sunglasses, I can get through the day better.”

His next career move, he said, will be to direct: “At some point I’ll have to do it or I’ll be a complete annoyance.” He said he had never aspired to be so well known, and one got the sense that even though he called the role of Merrick “a big swing,” disappearing into his lumpen skin, even metaphorically (there are no prosthetics in the play), might come as a relief.

Waiting back in his hotel room was an inversion table, a decompression device on which he has been lying upside down, like a bat, to recover from playing the contorted 5-foot-2 Merrick and once again become Bradley Cooper, with all that now entails.

“To straighten out your spine at the end of the day,” he said, “I find it very soothing.”

Correction:

Because of an online editing error, an earlier version of this article misidentified the date on which “The Elephant Man” will begin previews. They will begin on Nov. 7, not Oct. 31.

Correction:

An article last Sunday about Bradley Cooper, who is starring in a Broadway revival of “The Elephant Man,” referred incorrectly to the London address where Joseph Carey Merrick — the real Elephant Man — exhibited himself. The address is now a sari store — it is not, our sincerest apologies, “a sorry store.”